When I'm deciding which intergalactic data set to work with, I don't want to take any half measures. That's why I'm drawn to the Sloan Digital Sky Survey (SDSS). In their own words, "The Sloan Digital Sky Survey (SDSS) is one of the most ambitious and influential surveys in the history of astronomy." Sounds like their putting the project right up there with the greats like Galileo. You can bring this level of astronomical greatness into your app via the SDSS APIs: SDSS cone search & SDSS image cut-out.
A layperson like myself will probably feel a little lost when looking into this API. There's no easy to use developer console, but guess what, mapping the universe isn't easy either. You have to want it! If terms like right-ascension and declination crop up in your everyday conversations, and you're ready to deal with XML & SOAP you'll be in business in no time. Maybe you'd employ something like a Java framework that is fully conversant with WSDL defined services. You might have to jump through some hoops, but at least you don't have to build and operate your own telescope.